The basis of all recommended methods for obtaining position by using celestial bodies is the known altitude of the celestial body being observed. Accordingly, it is necessary to have a sextant, classic or with an artificial horizon, or some other device that can measure altitude. However, there is a way to obtain position using astronomical navigation without determining the altitude of a celestial body, and this method will be analysed in this paper. The introduced method requires only precise measurement of the azimuth, and is based on determining two positions close to the dead reckoning position and lying on the isoazimuthal curve, i.e. a curve of the same great circle azimuths of a celestial body. Furthermore, the model assumes that a part of this curve, between the selected positions, can be replaced by a straight line. Special attention will be given to the analysis of errors of the line of position for various azimuth errors and various dead reckoning (assumed) positions. It will also be shown how a modern Electronic Chart Display and Information System (ECDIS) can help in approximate position determination, knowing only the azimuths of celestial bodies.